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Equation 6 · Part 5 · Evaluating Trajectories, Not Answers

superscript

1−(1−p)kagainstpk.1 - (1-p)^k \qquad \text{against} \qquad p^k .
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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

The two quantities point in opposite directions as sampling increases. With per-attempt success probability p and independent attempts, compare 1−(1−p)kagainstpk1 - (1-p)^k \qquad \text{against} \qquad p^k . The first rises toward one; the second falls toward zero. They are computed from the same runs and answer entirely different questions, and reporting the first while the deployment depends on the second is the most common quiet misrepresentation in agent evaluation.

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.